The World Health Organisation (WHO) "does not function very well", David Cameron said as he criticised the speed of the response to the Ebola outbreak.
The Prime Minister said it should have been possible to "snuff out" the virus much quicker once the initial cases were detected in west Africa.
Mr Cameron's comments came as International Development Secretary Justine Greening visited Sierra Leone, where she announced new funding to protect the growing number of children and women affected by Ebola.
The Prime Minister's frustration with the WHO was made clear during an appearance in front of the Liaison Committee, made up of senior backbench MPs.
He agreed with International Development Select Committee chairman Sir Malcolm Bruce, who suggested that "we have to look at whether the WHO is fit for purpose".
The Prime Minister said he had proposed plans for a "crack team" of epidemiologists and experts to be sent to countries as soon as there is a health emergency.
Mr Cameron said: "There is a real question here: why was the world not faster in responding to Ebola?
"The thing about Ebola - because it's not airborne, it's passed by touch - if you get hold of it quicker you should be able to snuff out an occurrence of this disease much quicker.
"Everyone will have to take their share of responsibility, but I do think we need to learn the lessons.
"I argued at the G20 in Brisbane I think what we need is a standing team of epidemiologists and experts to be flown into a country when there's a problem, to assess how bad it is, to put the resources in and to sort it out.
"The WHO - I think (director general) Margaret Chan does a great job - but it does have some challenges.
"It's got these regional organisations that are, how can I put it, not the fastest moving. They are often packed with people who are not necessarily the right people.
"It doesn't function very well."
He added: "The whole world was a bit slow to wake up to this, everyone knew it was a problem but I think a lot people assumed that the WHO handled these things and they don't necessarily.
"Were there teams of scientists beating a path to my door saying, 'quick, wake up, everyone has got to see what a problem this is'? Not immediately, no."
Ms Greening announced a £2.5 million grant for Unicef, which will help make sure children who have lost family or whose parents are being treated for Ebola get the care and support they need.
She said: "Ebola not only takes people's lives, it leaves children without families and survivors facing rejection from their communities. Our work will ensure these people are not left behind once Ebola is defeated.
"Lots of children have suddenly seen their parents experience Ebola or at worst have lost one or both parents. We need to make sure that we keep them safe, help them cope with the terrible experiences they have gone through and, wherever possible, locate their extended families who can give them the care and love they need."